Effective failure behavior of an analytical and a numerical model for closed-cell foams

Abaqus, 2012 Abendroth, 2013, Determination of mechanical characteristics of ceramic open cell foams Altenbach, 2014, Phenomenological yield and failure criteria, 49 Altenbach, 2015, Classical and non-classical failure criteria, vol. 560, 1 Arezoo, 2011, The mechanical response of Rohacell foams at different length scales, J. Mater. Sci., 46, 6863, 10.1007/s10853-011-5649-7 Bardenheier, 1982 Becker, W., Kolupaev, V. A., 2014. Beschreibung der multiaxialen mechanischen Eigenschaften von isotropen Polymerschäumen auf der Basis von mikro- und makromechanischen Konzepten. Deutsche Forschungsgemeinschaft, Abschlussbericht BE 1090/27-1, KO 3382/6-1. Beckmann, 2015 Beckmann, 2012, Assessment of material uncertainties in solid foams based on local homogenization procedures, Int. J. Solids Struct., 49, 2807, 10.1016/j.ijsolstr.2012.02.033 Bitsche, 2005 Bowden, 1972, The plastic flow of isotropic polymers, J. Mater. Sci., 7, 52, 10.1007/BF00549550 Caddell, 1974, Pressure dependent yield criteria for polymers, Mater. Sci. Eng., 13, 113, 10.1016/0025-5416(74)90179-7 Chen, 1999, Effect of imperfections on the yielding of two-dimensional foams, J. Mech. Phys. Solids, 47, 2235, 10.1016/S0022-5096(99)00030-7 Chen, 1994, Relating the properties of foam to the properties of the solid from which it is made, Cellular Polym., 13, 16 Chen, 1991 Combaz, 2010 Combaz, 2010, Yield surface of polyurethane and aluminium replicated foam, Acta Materialia, 58, 5168, 10.1016/j.actamat.2010.05.053 Cuntze, 2015, Fracture failure surface of the foam Rohacell Daxner, 2003 Daxner, 2011, Finite element modeling of cellular materials, 47 Daxner, 2014, Plasticity of cellular metals (foams), 153 Daxner, 2006, Space-filling polyhedra as mechanical models for solidified dry foams, Mater. Trans., 47, 2213, 10.2320/matertrans.47.2213 Demiray, 2007 Demiray, 2007, Numerical determination of initial and subsequent yield surfaces of open-celled model foams, Int. J. Solids Struct., 44, 2093, 10.1016/j.ijsolstr.2006.06.044 Deshpande, 2001, Multi-axial yield behaviour of polymer foams, Acta Materialia, 49, 1859, 10.1016/S1359-6454(01)00058-1 Elmoutaouakkil, 2003, Three-dimensional quantitative analysis of polymer foams from synchrotron radiation x-ray microtomography, J. Phys. D, 36, A37, 10.1088/0022-3727/36/10A/308 Evonik Industries AG, 2014. URL www.rohacell.com. Fahlbusch, 2014, Non-linear material behavior and failure of closed-cell polymer foams Gänzler, 1970, Die polymeranaloge Bildung von Imidgruppen in Methacrylsäure/Methacrylnitril-Copolymeren, Die Angewandte Makromolekulare Chemie, 11, 91, 10.1002/apmc.1970.050110109 Gibson, 1999 Gong, 2005, Compressive response of open-cell foams. part I: Morphology and elastic properties, Int. J. Solids Struct., 42, 1355, 10.1016/j.ijsolstr.2004.07.023 Grenestedt, 1998, Influence of wavy imperfections in cell walls on elastic stiffness of cellular solids, J. Mech. Phys. Solids, 46, 29, 10.1016/S0022-5096(97)00035-5 Grenestedt, 1999, Effective elastic behavior of some models for perfect cellular solids, Int. J. Solids Struct., 36, 1471, 10.1016/S0020-7683(98)00048-1 Grenestedt, 2005, On interactions between imperfections in cellular solids, J. Mater. Sci., 40, 5853, 10.1007/s10853-005-5019-4 Grenestedt, 2000, Influence of cell wall thickness variations on elastic stiffness of closed-cell cellular solids, Int. J. Mech. Sci., 42, 1327, 10.1016/S0020-7403(99)00054-5 Grenestedt, 1998, Influence of cell shape variations on elastic stiffness of closed cell cellular solids, Scripta Materialia, 40, 71, 10.1016/S1359-6462(98)00401-1 Hohe, 2003 Hohe, 2005, A probabilistic approach to the numerical homogenization of irregular solid foams in the finite strain regime, Int. J. Solids Struct., 42, 3549, 10.1016/j.ijsolstr.2004.10.022 Hohe, 2010, On the potential of tungsten-vanadium composites for high temperature application with wide-range thermal operation window, J. Nuclear Mater., 400, 218, 10.1016/j.jnucmat.2010.03.007 Jang, 2008, On the microstructure of open-cell foams and its effect on elastic properties, Int. J. Solids Struct., 45, 1845, 10.1016/j.ijsolstr.2007.10.008 Jang, 2009, On the crushing of aluminum open-cell foams: Part II analysis, Int. J. Solids Struct., 46, 635, 10.1016/j.ijsolstr.2008.10.016 Kolupaev, 2009, Anwendung der Unified Strength Theory (UST) von Mao-Hong Yu auf unverstärkte Kunststoffe, 320 Kolupaev, 2014, Failure of hard foams under multiaxial loading, 183 Kolupaev, 2010, Geometrical-mechanical model applied to PVC-foams, 183 Kolupaev, 2011, Strength hypotheses for hard polymeric foams Kolupaev, 2011, Strength hypothesis applied to hard foams, Applied Mechanics and Materials, 70, 99, 10.4028/www.scientific.net/AMM.70.99 Kolupaev, 2014, Multi-axial tests on hard foams, 1 Kraatz, 2007 Lakes, 1993, Microbuckling instability in elastomeric cellular solids, J. Mater. Sci., 28, 4667, 10.1007/BF00414256 Landau, 2009 Laue, 1981 Luxner, 2007, Numerical simulations of 3d open cell structures–influence of structural irregularities on elasto-plasticity and deformation localization, Int. J. Solids Struct., 44, 2990, 10.1016/j.ijsolstr.2006.08.039 Maire, 2003, X-ray tomography applied to the characterization of cellular materials. Related finite element modeling problems, Comp. Sci. Technol., 63, 2431, 10.1016/S0266-3538(03)00276-8 Meguid, 2002, FE modelling of deformation localization in metallic foams, Finite Elements Anal. Design, 38, 631, 10.1016/S0168-874X(01)00096-8 Mills, 2010, Deformation mechanisms and the yield surface of low-density, closed-cell polymer foams, J. Mater. Sci., 45, 5831, 10.1007/s10853-010-4659-1 Mills, 2009, Finite element micromechanics model of impact compression of closed-cell polymer foams, Int. J. Solids Struct., 46, 677, 10.1016/j.ijsolstr.2008.09.012 Mills, 1999, The high strain compression of closed-cell polymer foams, J. Mech. Phys. Solids, 47, 669, 10.1016/S0022-5096(98)00007-6 Otsu, 1979, A threshold selection method from gray-level histograms, IEEE SMC, 9, 62 Papka, 1998, Experiments and full-scale numerical simulations of in-plane crushing of a honeycomb, Acta Materialia, 46, 2765, 10.1016/S1359-6454(97)00453-9 Pisarenko, 1976 Raghava, 1973, The macroscopic yield behaviour of polymers, J. Mater. Sci., 8, 225, 10.1007/BF00550671 Schlimper, 2014 Schröder, 1968, Verschäumbare Formmassen, Patentschrift Schwarz-Barać, 2003 Sehlhorst, 2009, Numerical investigations of foam-like materials by nested high-order finite element methods, Comput. Mech., 45, 45, 10.1007/s00466-009-0414-3 Shulmeister, 1998 Shutov, 1983, Foamed polymers. Cellular structure and properties, 155 Simone, 1998, The effects of cell face curvature and corrugations on the stiffness and strength of metallic foams, Acta Materialia, 46, 3929, 10.1016/S1359-6454(98)00072-X Simone, 1998, Effects of solid distribution on the stiffness and strength of metallic foams, Acta Materialia, 46, 2139, 10.1016/S1359-6454(97)00421-7 Storm, 2013, Geometry dependent effective elastic properties of open-cell foams based on Kelvin cell models, Adv. Eng. Mater., 15, 1292, 10.1002/adem.201300141 Ströhla, 2005, Einfluss von Strukturstörungen auf die elastisch-plastischen Materialparameter zellularer Werkstoffe, 137 Thomson (Lord Kelvin), 1887, On the division of space with minimum partitional area, Philosophical Mag., 24, 503, 10.1080/14786448708628135 Voigt, 1928 Wang, 2010, Experimental and numerical study of the elastic properties of PMI foams, J. Mater. Sci., 45, 2688, 10.1007/s10853-010-4250-9 Weaire, 1997 Wriggers, 2008 Youssef, 2005, Finite element modelling of the actual structure of cellular materials determined by X-ray tomography, Acta Materialia, 53, 719, 10.1016/j.actamat.2004.10.024 Zhang, 2015, Multi-axial brittle failure criterion using Weibull stress for open Kelvin cell foams, Int. J. Solids Struct., 10.1016/j.ijsolstr.2015.04.020 Źyczkowski, 1981